Question 1193300: the rectangles area is fours square units. the height plus twice the width is 6 units. step by step please
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area is 4 square units.
the height plus twice the width is 6 units.
H = height
W = width
area is H * W = 4
H + 2W = 6
in the second equation, solve for H to get:
H = 6 - 2W
in the first equation, replace H with (6 - 2W) to get:
H * W = 4 becomes (6 - 2W) * W = 4
simplify to get:
6 * W - 2W * W = 4
simplify further to get:
6W - 2W^2 = 4
add 2W^2 to both sides of the equation and subtract 6W from both sides of the equation to get:
0 = 2W^2 - 6W + 4
divide both sides of the equation by 2 to get:
0 = W^2 - 3W + 2
factor the quadratic equation and flip sides to get:
(W - 1) * (W - 2) = 0
solve for W to get:
W = 1 or W = 2
since H = 6 - 2W, then:
when W = 1, H = 4
when W = 2, H = 2
your solution is:
either W = 1 and H = 4, or W = 2 and H = 2
to confirm, replace H and W in the original equations with these values to get:
when W = 1 and H = 4, then:
area is H * W = 4 becomes 4 * 1 = 4 which is true.
H + 2W = 6 becomes 4 + 2 = 6 which is also true.
when W = 2 and H = 2, then:
area is H * W = 4 becomes 2 * 2 = 4 which is true.
H + 2W = 6 becomes 2 + 4 = 6 which is also true.
let me know if you have any questions, or need further clarification.
theo
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